Question
$$\frac{5}{x-3} = \frac{x+4}{x}$$
Answer
$$ \begin{matrix}x_1 = -2 & x_2 = 6 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{x-3} &= \frac{x+4}{x}&& \text{multiply ALL terms by } \color{blue}{ (x-3)x }. \\[1 em](x-3)x\cdot\frac{5}{x-3} &= (x-3)x \cdot \frac{x+4}{x}&& \text{cancel out the denominators} \\[1 em]5x &= x^2+x-12&& \text{move all terms to the left hand side } \\[1 em]5x-x^2-x+12 &= 0&& \text{simplify left side} \\[1 em]-x^2+4x+12 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+4x+12 = 0 $ is a quadratic equation.
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